Recent efforts have been directed towards the development of microscale assay methods in which various chemical and biological processes may be examined in rapid succession and with small amounts of material. For example, microfluidic chips, which are chips of glass, silica or plastic contain a network of microscale channels through which fluids and chemicals are moved in order to perform the experiment. These chips use minute quantities of fluids or other materials, controllably flowed and/or directed, to generate highly reproducible and rapidly changeable microenvironments for control of chemical and biological reaction conditions, enzymatic processes, etc.
Microfluidic devices use a small volume of material. A plug of the material of interest, such as a molecule, compound, or biological compound or molecule such as a protein, analyte, or DNA molecule is introduced to a conduit and observed at least at some point along the channel. Several plugs of a variety of compounds are typically introduced into the same conduit separated by sufficient solvent or buffer material to distinguish the two plugs. However, as a plug of material moves along a conduit, a variety of forces causes the material of interest to disperse from a concentrated discrete plug into adjacent volumes of buffer or other solvent that separate the plug of material from adjacent sample plugs introduced into the conduit. Such forces include the laminar or parabolic velocity profile of a plug of material in a conduit and the molecular diffusivity of the particular material within a particular buffer or other solvent. Due to dispersion, a plug of material having a certain length and a certain concentration at the beginning of the conduit will have a longer length and be less concentrated at the end of the conduit.
One advantage of microfluidic devices is that a large variety of small plugs can be introduced and monitored within a conduit in rapid succession. The more plugs of material directed into a conduit at a time, the more tests can be run in a smaller amount of time. If the plugs of material are introduced too closely, however, dispersion may cause the solute in one sample plug to overlap the solute of a second adjacent sample plug by the time the plugs travel to the opposite end of the conduit. Thus, it is helpful to be able to adequately predict how the length of a plug will increase due to dispersion to maximize throughput, i.e., maximize the number of different samples plugs introduced to the conduit in a minimum amount of time, and minimize cross-contamination of adjacent sample plugs. U.S. Pat. No. 6,150,119, which is incorporated herein by reference in its entirety, provides further discussion of maximizing throughput.
Further, in very small microchannels, inertial effect, turbulence and other forces that typically affect streamlines in larger channels become negligible. Fluids flowing through a microchannel experience near laminar flow, or flow in distinct layers or streamlines. With laminar flow, streamlines do not intermix, other than by diffusion, across streamlines or between contacting streams. Thus, an accurate determination of molecular diffusivity for a particular sample is important for optimal development and use of microfluidic devices and techniques, particularly for predicting particle dispersion.
Taylor developed a method to measure molecular diffusion based on the mass flux in a capillary tube. See e.g., Taylor, Sir Geoffery, F. R. S. Conditions of soluble matter in solvent flowing slowly through a tube, Proc. Roy. Soc. (London) 219A:186–203 (1953) and Taylor, Sir Geoffrey, F. R. S., Conditions under which dispersion of a solute in a stream of solvent can be used to measure molecular diffusion, Proc. Roy. Soc. (London) A225: 473–477 (1954). In particular, he determined that the mass flux along the length of a capillary tube is a sum of convection forces and molecular diffusion. Aris developed a formula based on the work of Taylor for calculating the apparent diffusion coefficient, K. Aris, R., On the dispersion of a solute in a fluid flowing through a tube, Proc. Roy. Soc. (London) A235:67–77 (1956). However, the Taylor-Aris formula was useful only for circular tubes and other shaped conduits with a known radius. However, it must be adapted for non-circular tubes, rectangular channels or other irregular shaped conduits, such as microfluidic channels. See Chatwin, P. C., et al., The effect of aspect ratio on longitudinal diffusivity in rectangular channels, Journal of Fluid Mechanics 120:347–358 (1982). Because the Taylor-Aris dispersion formula requires complicated and rigorous viscosity calculations to determine the average velocity and requires making various assumptions in order to calculate the molecular diffusivity, the method is typically effective only for low velocity flow and small radial distances. Nonetheless, the method is still often used today for measuring molecular diffusivities.
Others have tried various other calculations based on the Taylor-Aris formulation. See e.g., Michael S. Bello, et al., Use of Taylor-Aris Dispersion for Measurement of a Solute Diffusion Coefficient in Thin Capillaries, Science 266:773–776 (1994). However, these methods still require extra steps to determine velocity.
Still others have determined molecular diffusivities by measuring a stream of solute in a single microchannel. See e.g., Andrew E. Kamholz, et al., Optical Measurement of Transverse Molecular Diffusion in a Microchannel, Biophys J 80(4):1967–1972 (April 2001). Further, U.S. Pat. Nos. 5,872,710 and 6,541,213, both to Weigl et al, and U.S. Pat. No. 5,932,100 to Yager et al., which are all incorporated herein by reference in their entirety, discuss how to manipulate diffusivities in a single microchannel to separate large and small particles, because larger particles diffuse more slowly than small particles. In general, these references teach having a sample solute stream and a blank stream, such as a stream of just a solvent or buffer, flow in distinct streamlines through a single microchannel. Smaller particles diffuse across streamlines creating a diffusion profile along the length of the channel. In order to measure the amount and rate of diffusion, small changes in concentrations must be measured in a single microchannel (generally in the middle of the channel) having a large background signal because the microchannel contains both diffused particles and undiffused particles. Further, these separation methods occur with both the blank stream and the sample stream having the same flowrate.